MECHANICS OF
MACHINERY
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Dynamics
Kinematics:
• It deals with the relative motions of different parts of a
mechanism without taking into consideration the forces
producing the motions.
• Thus, it is the study, from a geometric point of view, to know
the displacement, velocity and acceleration of a part of a
mechanism.
Kinetics:
• Studies the forces on the system which is in motion.
• It deals with inertia forces which arises from the combined
effect of mass and motion of the machine parts
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Kinematics
Kinetics
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Mechanism and Machine
Mechanism (a fundamental unit for kinematic study)
• If a number of bodies are assembled in such a way that the
motion of one causes constrained and predictable motion to
the others, it is known as a mechanism.
• A mechanism transmits and modifies a motion.
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Mechanism and Machine
Machine
• A machine is a mechanism or a combination of mechanisms
which, apart from imparting definite motions to the parts, also
transmits and modifies the available mechanical energy into
some kind of desired work.
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Mechanism and Machine
Mechanisms
Can crusher
Simple press
Rear-window
wiper
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Machines
Bulldozer
Amusement
Park Ride
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Mechanism and Machine
Machine
Mechanism
Machine modifies mechanical work
Mechanism transmits and modifies
motion
A machine is a practical development of
any mechanism
A machine may have number of
mechanism for transmitting mechanical
work or power
A mechanism is a part of a machine
A mechanism is a skeleton outline of the
machine to produce motion between
various links.
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Terms and definitions
• Rigid body
• A body is said to be rigid if it under the action of forces, it does not suffer
any distortion.
• i.e , the distance between any points on the body remains constant
• Semi rigid body
• Normally are flexible
• Under loading condition acts as rigid body for limited purpose
• Also called as resistant bodies
• Eg. Belt under tension, fluid on compression
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• Kinematic link
• A resistant body or a group of resistant bodies with rigid connections
preventing their relative movement is known as a link.
• It can be also defined as a member or a combination of members of a
mechanism, connecting other members and having motion relative to them
• Links can be classified into binary, ternary and quaternary depending upon
their ends on which revolute or turning pairs can be placed
• It must contain two or more nodes
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Terms and definitions
• Joint
• It is the connection between two or more links which allows some motion
between the connecting links.
• Kinematic pair
• The two links or elements of a machine, when in contact with each other, are said
to form a pair.
• If the relative motion between them is completely or partially constrained (i.e. in
a definite direction), the pair is known as kinematic pair.
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Constrained motion (or relative motion) can be broadly classified into three
types.
• Completely constrained motion
• Incompletely constrained motion
• Partially (or successfully) constrained motion
• Completely constrained motion is a type of constrained motion in which relative
motion between the links of a kinematic pair occurs in a definite direction by
itself, irrespective of the external forces applied.
• In incompletely constrained motion, the relative motion between the links
depend on the direction of external forces acting on them.
• Motion of a shaft inside a circular hole. Depending on the direction of
external forces applied, the shaft may slide or turn (or do both) inside the
circular hole
• A kinematic pair is said to be partially or successfully constrained if the relative
motion between its links occurs in a definite direction, not by itself, but by some
other means.
• Piston reciprocating inside a cylinder in an internal combustion engine.
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• Degree of freedom
• Number independent motions(translational or rotary) required to
completely specify the relative movement of a pair.
• If DOF = + ve (mechanism)
• If DOF = zero (structure)
• Structure( statics)
• Mechanism (kinematics)
• Machine ( kinetics )
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Classification of kinematic pair
• Based on type of contact between the elements
• Point, line, surface
• If the type contact is point or line type they are called as the higher pair
• If the contact type is area or surface , they are called as lower pair
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Classification of kinematic pair
• Based on the nature of mechanical constraints
• Closed pair- When the elements of a pair are held together mechanically.
• Unclosed pair- When two links of a pair are in contact due to the force of
gravity or spring force
• All lower pair and some higher pairs are closed pair
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Classification of kinematic pair
• According to nature of relative motion
Sliding pair
Turning pair
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Classification of kinematic pair
• According to nature of relative motion
Screw pair
Rolling pair
Spherical pair
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Classification of kinematic pair
• Based on degree of freedom
• Degree of freedom of a pair is defined as the number of independent
relative motion, both translational and rotational
Classification of kinematic pairs
a) Sphere- plane
No. of restraints= 1
Restraints on
Translatory motion= 1
Rotary motion=0
b) Sphere- cylinder
No. of restraints= 2
Restraints on
Translatory motion= 2
Rotary motion=0
c) Cylinder- plane
No. of restraints= 2
Restraints on
Translatory motion= 1
Rotary motion=1
d) Spheric
No. of restraints= 3
Restraints on
Translatory motion= 3
Rotary motion=0
e) Sphere- slotted cylinder
No. of restraints= 3
Restraints on
Translatory motion= 2
Rotary motion=1
f) Prism- plane
No. of constraints=3
Restraints on
Translatory motion= 1
Rotary motion=2
g) Slotted- spheric
No. of constraints=4
Restraints on
Translatory motion= 3
Rotary motion=1
h) Cylinder
No. of restraints=4
Restraints on
Translatory motion= 2
Rotary motion=2
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Degree of freedom for various joints
Type of joint
Nature of motion
DOF
Hinges(Revolute)
Turning
1
Slider
Pure sliding
1
Cylindrical, cam ,
gear, ball bearing
Turning and sliding
Turning and rolling
2
Rolling contact
Pure rolling
1
Spheric
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• Kinematic chain
• An assemblage of links and joints, interconnected in a way to provide a
controlled output motion in response to a supplied input motion.
• Motion of one link will create relative and definite motion on other link.
• A redundant chain does not allow any motion of a link relative to the
other.
• A kinematic chain with one link fixed is called as mechanism
• A redundant chain having one link fixed to ground is called structure
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In short…..
• A kinematic link is defined as a resistant body or a group of resistant
bodies with rigid connections preventing their relative movement.
• A kinematic pair is a joint of two links having relative motion
between them.
• A kinematic chain is an assembly of links in which the relative
motions of the links are possible and the motion of each relative to
the other is definite.
• If one of the links of a kinematic chain is fixed to the ground and the
motions of any of the movable links results in definite motions of
others, then it is known as mechanism.
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• A mechanism may consist of a number of pairs belonging to
diff. classes having different no. of restraints
• Ranging from single order mechanism (one restraints) to fifth
order(with five restraint)
• Sixth order mechanism is impossible
• Mobility of a mechanism defines the number of degrees of
freedom a mechanism posses.
• For space mechanism
• F= 6(N-1) - 5 P1- 4P2- 3P3 - 2P4 – P5
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• Most of mechanism are 2-D (i.e , translational along two direction,
and rotation about an axis)
• So, eqn becomes,
• F= 3(N-1) - 2P1 – P2
• Known as Gruebler’s criterion for dof of planar mechanism
• For linkages with only turning pair,P2 = 0
• So eqn becomes,
• F= 3(N-1) - 2P1
• Known as Kutzback’s criterion
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• For most of the mechanism the dof of the mechanism is one.
• So
i.e,
1 = 3(N-1) - 2P1
2P1 = 3N – 4
• If N = 4, then P1 = 4
(no excess turning pair)
• If N = 6, then P1 = 7
(one excess turning pair)
• If N = 8, then P1 = 10
(two excess turning pair)
• So as no. of links increases, excess turning pair is req.
• So instead of binary link use of ternary or quaternary link is encouraged
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• N=4
• P1=4
• P2=0
• F=3(N-1)- 2P1-1P2 =
3(3)- 2(4)-1(0)= 1
• Therefore the mechanism has 1 DOF
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• N=4
• P1=3
• P2=1
• F=3(N-1)- 2P1-1P2 =
3(3)- 2(3)-1(1)= 2
• Therefore the mechanism has 2 DOF
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2
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Four bar (link) mechanism
• Simple and versatile
• Necessaties
• The length of longest link must be less than the sum of lengths of other
three links.
• Grashof’s condition
• If (s + l) ≤ (a+b)
• Then the linkage is grashof and at least one link may be capable of
complete revolution.
• This is Class I Kinematic chain
• If not , its non- grashof known as
• Class II Kinematic chain
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• Kinematic Inversions – Process of choosing different links of a
kinematic chain to be fixed or ground to obtain new
mechanisms
• No of kinematic inversions is equal to no of links in the
kinematic chain
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Inversions of four link mechanism
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Oil pump
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Slider crank mechanism
• Kinematic Inversions – Process of choosing different links of a
kinematic chain to be fixed or ground to obtain new
mechanisms
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First Inversion
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Second inversion
• Applications • Whitworth Quick Return Mechanism
• Rotary Engine
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• Rotary Engine
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Third inversion
• Oscillating cylinder
• Link 4 is made in the form of cylinder and a piston fixed to a rod as link 1
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Crank & slotted lever quick return
mechanism
• Cylinder of oscillating cylinder is replaced by link made in the
form of guide
• Piston and link replaced by slider
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Fourth inversion
Fourth inversion is obtained by fixing link 4 of slider crank
mechanism
Application: Hand pump
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Whitworth quick return mechanism
Crank and slotted lever mechanism
1. Crank of whitworth is longer than
fixed link
1. Fixed link is longer than crank
2.The coupler link makes complete
rotation about the pivot joint of fixed
link
2. Coupler link oscillates about the
pivot
3. For same dislacement, Coupler link
connected to tool post is connected at
the other side of main coupler link
with respect to slider
3. Coupler link connected to tool post
is connected at the same side of main
coupler link with respect to slider, but
after the extreme position of slider
Double slider crank mechanism
• Four bar chain having two turning and sliding pairs such that
two pairs of the same kind are adjacent is known as double
slider crank chain
Link 4
Link 3
Link 1
Link 2
First inversion
Application- Elliptical trammel
Link 1- fixed
Adjacent pairs link 2&3, link3&4– turning pairs
Adjacent pairs link 1&2, link1&4– sliding pairs
Link 4
Link 3
Link 1
Link 2
Scotch yoke ( Second Inversion )
• A scotch- yoke mechanism is used to convert the rotary motion to sliding motion.
• If any slide blocks of the first inversion is fixed second inversion is obtained
• As the crank 3 rotates the horizontal portion of the link 1 slides in the fixed link 4
• Used in control valve actuators in high pressure oil and gas pipe lines
Third inversion
Application- Oldham’s coupling
• Link 3 of the first inversion is fixed and link 1 is free to move
Oldham’s coupling
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Couplers curves
• For most of the mechanisms, output obtained from path traced
by points on coupler link.
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Couplers curves
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APPROXIMATE STRAIGHT LINE MECHANISM
(a) Watt’s Straight Line Mechanism (1784)
L1:L2:L3 = 2:1:2
• Link AB & DE act as levers and ends A & E are fixed.
• On small displacement of the mechanism, the tracing point P traces the shape
of number 8 , a portion of which will be approximately straight , and hence also
an example for approximate straight line mechanism
(b) Chebyshev linkage
L1:L2:L3:L4 = 4:5:2:5
•The Chebyshev linkage is a mechanical linkage that converts rotational motion to
approximate straight-line motion
•It was invented by the 19th century mathematician Pafnuty Chebyshev who studied
theoretical problems in kinematic mechanisms
(c) Hoekens linkage
•The Hoekens linkage is a four-bar mechanism that converts rotational
motion to approximate straight-line motion with approximate constant
velocity.
d) Robert’s mechanism
AO=BQ, AC=BC
CP perpendicular to AB
P is the tracing point
ACCURATE STRAIGHT
LINE MECHANISM
Peaucellier–Lipkin linkage
The Peaucellier–Lipkin linkage invented in 1864, was the first
planar linkage capable of transforming rotary motion into
perfect straight-line motion and vice versa
Hart Mechanism
•O O1 is the fixed link
•O1Q is the rotating link
•Point Q moves in a circle with O1 and radius O1Q
•ABCD is a trapezium so that AB=CD; BD parallel to AC
•BO/BA= BQ/BC=DP/DA
•Point P describes the straight line perpendicular to OO1
Scott- Russel Mechanism
OB=BS=BC
CO perpendicular to OS
S moves in a straight line along
OS
INTERMITTENT
MOTION MECHANISM
Ratchets and Escapements
•There are different forms of ratchets and escapements used in engineering
practices
•They are used in locks, clock works, jacks and many other mechanism
requiring some form of intermittent motion
Fig (a) shows one kind of ratchets which allows
the motion of the gear in one direction
Above figure is an example for deadbeat escapement used
commonly in pendulum clocks
A gravity escapement uses a small weight or a weak spring to
give an impulse directly to the pendulum
Grass hopper escapement
Geneva mechanism
•It is an intermittent motion mechanism
•Consists of a driving wheel D carrying a pin P which engages in a slot of the follower F
•During one quarter revolution of the driving plate, the pin and follower remain in
contact and hence the follower is turned by one quarter turn
•During the remaining time of one revolution of the driver , the follower remains at rest
locked in position by the circular arc
Steering gear mechanism
Fundamental Equation of Correct Steering
Types of Steering Gear
•Davis steering gear (which has sliding pairs)
•Ackermann steering gear (which has turning pairs)
Davis steering gear mechanism
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Ackermann steering gear
Hooke’s joint or Universal coupling
•Hooke’s joint is a device that connects two shafts whose axes are neither coaxial nor
parallel but intersect at a point
•Used to transmit power from the engine to the rear axle of an automobile
•Transmission of drives to different spindle in multiple drilling machine
•Knee joint in a milling machine
•Transmission of torque in rolling mills
Hooke’s joint or Universal coupling
• When driver shaft rotates with uniform speed,
• The driven shaft rotates at continuously varying speed
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• As a mechanism moves over a range of motion its geometry changes. If we are using
a mechanisms to transmit torque, or force then we must consider the ratio between
the input and output force in various positions.
• Mechanical Advantage
• The advantage gained by the use of a mechanism in transmitting force
• The ratio of the force that performs the useful work of a machine to the force
that is applied to the machine
• Transmission angle
• Transmission angle is the angle between the coupling member and the
output member in a mechanism.
• As this angle approaches ±90°, the mechanical advantage of the mechanism
typically increases.
• Toggle position
• Toggle positions occur when the mechanical advantage has near infinite.
• Mechanisms which utilizes this is position is called as toggle mechanism.
• Used for stone crushers
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• PANTOGRAPH
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Dwell mechanism